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You do not necessarily need the common prime factors when finding the greatest common factor, but with large numbers or numbers for which you cannot easily determine all the factors, using prime factorization to determine the greatest common factor is the easiest method. The greatest common factor can then be determined by multiplying the common prime factors together.

For example, when trying to find the greatest common factor of 2144 and 5672, finding all their possible factors to compare could be difficult. So, it is easier to find their prime factors, determine the prime factors they have in common, and then multiply the common prime factors to get the greatest common factor.

For descriptions and examples of finding the greatest common factor, see the "Related Questions" links below.

Q: Why do you need the common prime factors when finding the greatest common factor?

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Short answer: There are none. There is neither a greatest common factor nor common factors of a single number, such as ??, because there cannot be any form of common factor without two or more numbers to compare. Common factors are factors that the numbers being compared have in common. The greatest common factor is the largest factor that all the numbers being compared have in common. Thus, since there are not two or more numbers to compare, there are neither common factors nor a greatest common factor. Examples: The common factors of 1 and 3 are only 1; the greatest common factor is 1. The common factors of 1 and 111 are only 1; the greatest common factor is 1. Note: Since the only factor of 1 is 1, when finding the greatest common factor of 1 and another number, the only possible common factor and greatest common factor is 1.

Neither 16 nor 36 have a greatest common factor. There is neither a greatest common factor nor common factors of a single number, such as 16, because there cannot be any form of common factor without two or more numbers to compare. Common factors are factors that the numbers being compared have in common. The greatest common factor is the largest factor that all the numbers being compared have in common. Thus, since there are not two or more numbers to compare, there are neither common factors nor a greatest common factor. However, there is a greatest common factor of the pair of 16 and 36. It is 4. See the related question for an explanation on finding the greatest common factor of 16 and 36.

24 is not the greatest common factor of any single number. Common factors are the factors that two or more numbers have in common. The greatest common factor is the largest factor that two or more numbers have in common. There cannot be any common factors or a greatest common factor of a single number. There must be at least two number for common factors and a greatest common factor. Example: The greatest common factor of 24 and 48 is 24. The greatest common factor of 60 and 144 is 24. The greatest common factor of 240 and 264 is 24.

Short answer: There are none. There is neither a greatest common factor nor common factors of a single number, such as 35, because there cannot be any form of common factor without two or more numbers to compare. Common factors are factors that the numbers being compared have in common. The greatest common factor is the largest factor that all the numbers being compared have in common. Thus, since there are not two or more numbers to compare, there are neither common factors nor a greatest common factor. Examples: The common factors of 10 and 35 are 1 and 5; the greatest common factor is 5. The common factors of 21 and 35 are 1 and 7; the greatest common factor is 7. The common factors of 35 and 45 are 1 and 5; the greatest common factor is 5. The common factors of 35 and 49 are 1 and 7; the greatest common factor is 7. The common factors of 35 and 61 are only 1; the greatest common factor is 1.

The greatest common factor is the largest of the common factors.

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Finding the greatest common factor helps when you are reducing fractions.

By finding the factors in both numbers and then finding the one that is greatest in common. For example the G.C.F for 45 and 36 is 9.

Short answer: There are none. There is neither a greatest common factor nor common factors of a single number, such as ??, because there cannot be any form of common factor without two or more numbers to compare. Common factors are factors that the numbers being compared have in common. The greatest common factor is the largest factor that all the numbers being compared have in common. Thus, since there are not two or more numbers to compare, there are neither common factors nor a greatest common factor. Examples: The common factors of 1 and 3 are only 1; the greatest common factor is 1. The common factors of 1 and 111 are only 1; the greatest common factor is 1. Note: Since the only factor of 1 is 1, when finding the greatest common factor of 1 and another number, the only possible common factor and greatest common factor is 1.

Neither 16 nor 36 have a greatest common factor. There is neither a greatest common factor nor common factors of a single number, such as 16, because there cannot be any form of common factor without two or more numbers to compare. Common factors are factors that the numbers being compared have in common. The greatest common factor is the largest factor that all the numbers being compared have in common. Thus, since there are not two or more numbers to compare, there are neither common factors nor a greatest common factor. However, there is a greatest common factor of the pair of 16 and 36. It is 4. See the related question for an explanation on finding the greatest common factor of 16 and 36.

1,2,5,10 are the common factors, and the Greatest Common Factor is 10.

24 is not the greatest common factor of any single number. Common factors are the factors that two or more numbers have in common. The greatest common factor is the largest factor that two or more numbers have in common. There cannot be any common factors or a greatest common factor of a single number. There must be at least two number for common factors and a greatest common factor. Example: The greatest common factor of 24 and 48 is 24. The greatest common factor of 60 and 144 is 24. The greatest common factor of 240 and 264 is 24.

Short answer: There are none. There is neither a greatest common factor nor common factors of a single number, such as 35, because there cannot be any form of common factor without two or more numbers to compare. Common factors are factors that the numbers being compared have in common. The greatest common factor is the largest factor that all the numbers being compared have in common. Thus, since there are not two or more numbers to compare, there are neither common factors nor a greatest common factor. Examples: The common factors of 10 and 35 are 1 and 5; the greatest common factor is 5. The common factors of 21 and 35 are 1 and 7; the greatest common factor is 7. The common factors of 35 and 45 are 1 and 5; the greatest common factor is 5. The common factors of 35 and 49 are 1 and 7; the greatest common factor is 7. The common factors of 35 and 61 are only 1; the greatest common factor is 1.

The greatest common factor is the largest of the common factors.

Short answer: There are none. There is neither a greatest common factor nor common factors of a single number, such as 34, because there cannot be any form of common factor without two or more numbers to compare. Common factors are factors that the numbers being compared have in common. The greatest common factor is the largest factor that all the numbers being compared have in common. Thus, since there are not two or more numbers to compare, there are neither common factors nor a greatest common factor. Examples: The common factors of 12 and 34 are 1 and 2; the greatest common factor is 2. The common factors of 34 and 40 are 1 and 2; the greatest common factor is 2. The common factors of 34 and 85 are 1 and 17; the greatest common factor is 17. The common factors of 34 and 91 are only 1; the greatest common factor is 1.

The common factors are: 1, 3 The Greatest Common Factor (GCF) is: 3

The common factors are: 1, 3 The Greatest Common Factor (GCF) is: 3

There is neither a greatest common factor nor common factors of a single number, such as 10, because there cannot be any form of common factor without two or more numbers to compare. Common factors are factors that the numbers being compared have in common. The greatest common factor is the largest factor that all the numbers being compared have in common. Thus, since there are not two or more numbers to compare, there are neither common factors nor a greatest common factor. The factors of 10 are 1, 2, 5, and 10. The prime factors of 10 are 2 and 5. Examples: The common factors of 10 and 35 are 1 and 5; the greatest common factor is 5. The common factors of 10 and 38 are 1 and 2; the greatest common factor is 2. The common factors of 10 and 90 are 1, 2, 5, and 10; the greatest common factor is 10. The common factors of 10 and 108 are 1 and 2; the greatest common factor is 2.